Add: page rank

21.PageRank/PageRank.py

@@ -0,0 +1,45 @@
+import numpy as np
+import sys
+import os
+from pathlib import Path
+sys.path.append(str(Path(os.path.abspath(__file__)).parent.parent))
+from utils import *
+
+def pageRank(graph, d, max_iteration=1000, epsilon=1e-8):
+    """
+    given a n * n link graph
+    graph[i, j] = 1 means that there is a link from i to j
+    d is the proportion of neighbours in the definition of page rank
+    return the probablisitic for a user visiting each page
+    """
+    n, _ = graph.shape
+    p = np.ones(n) / n
+    graph /= (graph.sum(axis=-1, keepdims=True) + epsilon)
+    graph = graph.T
+    for i in range(max_iteration):
+        pre_p = p
+        p = d * graph @ p + (1 - d) / n
+        if max(p - pre_p) < epsilon:
+            break
+    return p
+
+if __name__ == '__main__':
+    def demonstrate(graph, d, desc):
+        print(desc)
+        p = pageRank(graph, d=d)
+        print('The probability of each node is', np.round(p, 2))
+
+    graph = np.array(
+        [[0, 1, 1, 1],
+         [1, 0, 0, 1],
+         [0, 0, 1, 0],
+         [0, 1, 1, 0]]
+    ).astype(float)
+    demonstrate(graph, .8, 'Example 1')
+
+    graph = np.array(
+        [[0, 1, 1],
+         [0, 0, 1],
+         [1, 0, 0]]
+    ).astype(float)
+    demonstrate(graph, .85, 'Example 2')